The first stage of the protostellar collapse is isothermal at \(\sim 10\)  K until density reaches \(\sim 10^{-13}\)  g cm\(^{-3}\) . At this point, the dust-gas mixture becomes opaque to its own thermal radiation and the temperature rises as a core forms and contracts slowly [1]}. At 2000 K, the dissociation of H\(_2\)  molecules absorbs energy, allowing a rapid second collapse that leads to the creation of the protostar when all H\(_2\)  is depleted. The thermal ionization of hydrogen occurs during the second collapse, and all hydrogen becomes ionized early in the protostar's life, provoking a drop in resistivities to virtually zero [2]}. Accounting for the thermal ionization of hydrogen is therefore critical to accurately describe the transition between the first core and the protostar, and thus from the nonideal to ideal MHD regime.
